Electrophoretic traveling waves

Authors:
P. C. Fife, O. A. Palusinski and Y. Su

Journal:
Trans. Amer. Math. Soc. **310** (1988), 759-780

MSC:
Primary 35Q20; Secondary 76R99, 92A40

MathSciNet review:
973176

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: An existence-uniqueness-approximability theory is given for a prototypical mathematical model for the separation of ions in solution by an imposed electric field. The separation is accomplished during the formation of a traveling wave, and the mathematical problem consists in finding a traveling wave solution of a set of diffusion-advection equations coupled to a Poisson equation. A basic small parameter appears in an apparently singular manner, in that when (which amounts to assuming the solution is everywhere electrically neutral), the last (Poisson) equation loses its derivative, and becomes an algebraic relation among the concentrations. Since this relation does not involve the function whose derivative is lost, the type of "singular" perturbation represented here is nonstandard. Nevertheless, the traveling wave solution depends in a regular manner on , even at ; and one of the principal aims of the paper is to show this regular dependence.

**[Ag]**D. Agin,*Electroneutrality and electrodiffusion in the squid axon*, Proc. Nat. Acad. Sci. U.S.A.**57**(1967), 1232-1238.**[Al]**R. A. Alberty,*Moving boundary systems formed by weak electrolytes*:*Theory of simple systems formed by weak acids and bases*, J. Amer. Chem. Soc.**72**(1950), 361.**[ABR]**R. A. Arandt, J. D. Bond, and L. D. Roper,*Electrical approximate solutions of steady-state electrodiffusion for a simple membrane*, J. Theoret. Biol.**34**(1972), 265-276.**[B]**M. Bier et al.,*Electrophoresis*:*Mathematical modeling and computer simulation*, Science**219**(1983), 281.**[CB]**M. Coxon and M. J. Binder,*Isotachophoresis theory*, J. Chromatogr.**95**(1974), 133.**[CL]**Earl A. Coddington and Norman Levinson,*Theory of ordinary differential equations*, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. MR**0069338****[De]**Z. Deyl, ed.,*Electrophoresis*:*A survey of techniques and applications*, Elsevier, Amsterdam, 1979.**[Do]**V. P. Dole,*A theory of moving boundary systems formed by strong electrolytes*, J. Amer. Chem. Soc.**67**(1945), 119.**[K]**F. Kohlrausch,*Ueber Concentrations-Verschiebungen durch Electrolyse im Inneren von Losungen und Losungsgemischen*, Ann. Physik**62**(1897), 209.**[SP]**D. A. Saville and O. A. Palusinski,*Theory of electrophoretic separations*, Parts 1 and 2, AIChE J.**32**(1986).

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
35Q20,
76R99,
92A40

Retrieve articles in all journals with MSC: 35Q20, 76R99, 92A40

Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1988-0973176-4

Keywords:
Electrophoresis,
traveling waves,
singular perturbation,
diffusion-advection equations,
Schauder fixed points

Article copyright:
© Copyright 1988
American Mathematical Society